<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>, and an integer <code>k</code>.</p>

<p>You are allowed to perform some operations on <code>nums</code>, where in a single operation, you can:</p>

<ul>
	<li>Select the two <strong>smallest</strong> integers <code>x</code> and <code>y</code> from <code>nums</code>.</li>
	<li>Remove <code>x</code> and <code>y</code> from <code>nums</code>.</li>
	<li>Insert <code>(min(x, y) * 2 + max(x, y))</code> at any position in the array.</li>
</ul>

<p><strong>Note</strong> that you can only apply the described operation if <code>nums</code> contains <strong>at least</strong> two elements.</p>

<p>Return the <strong>minimum</strong> number of operations needed so that all elements of the array are <strong>greater than or equal to</strong> <code>k</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [2,11,10,1,3], k = 10</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<ol>
	<li>In the first operation, we remove elements 1 and 2, then add <code>1 * 2 + 2</code> to <code>nums</code>. <code>nums</code> becomes equal to <code>[4, 11, 10, 3]</code>.</li>
	<li>In the second operation, we remove elements 3 and 4, then add <code>3 * 2 + 4</code> to <code>nums</code>. <code>nums</code> becomes equal to <code>[10, 11, 10]</code>.</li>
</ol>

<p>At this stage, all the elements of nums are greater than or equal to 10 so we can stop.&nbsp;</p>

<p>It can be shown that 2 is the minimum number of operations needed so that all elements of the array are greater than or equal to 10.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,1,2,4,9], k = 20</span></p>

<p><strong>Output:</strong> <span class="example-io">4</span></p>

<p><strong>Explanation:</strong></p>

<ol>
	<li>After one operation, <code>nums</code> becomes equal to <code>[2, 4, 9, 3]</code>.&nbsp;</li>
	<li>After two operations, <code>nums</code> becomes equal to <code>[7, 4, 9]</code>.&nbsp;</li>
	<li>After three operations, <code>nums</code> becomes equal to <code>[15, 9]</code>.&nbsp;</li>
	<li>After four operations, <code>nums</code> becomes equal to <code>[33]</code>.</li>
</ol>

<p>At this stage, all the elements of <code>nums</code> are greater than 20 so we can stop.&nbsp;</p>

<p>It can be shown that 4 is the minimum number of operations needed so that all elements of the array are greater than or equal to 20.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
	<li>The input is generated such that an answer always exists. That is, after performing some number of operations, all elements of the array are greater than or equal to <code>k</code>.</li>
</ul>
